Published papers (in order of publication date):
Quartic polynomials in two variables do not represent all non-negative integers, joint work with Shuntaro Yamagishi, to appear in Journal of the European Mathematical Society, DOI 10.4171/JEMS/1697
Heights and quantitative arithmetic on stacky curves, joint work with B. Nasserden, Canadian Journal of Mathematics. (2) 77 (2025), 481–534. DOI: https://doi.org/10.4153/S0008414X24000075
Prime values of f (a, b^2) and f (a, p^2), f quadratic, Algebra and Number Theory, (9) 18 (2024), 1619-1679. DOI: 10.2140/ant.2024.18.1619
Density of power-free values of polynomials, II, with Kostadinka Lapkova, Journal of Number Theory 265 (2024), 20-35. DOI: https://doi.org/10.1016/j.jnt.2024.06.010
Elliptic curves with a rational 2-torsion point ordered by conductor and the boundedness of average rank, Advances in Mathematics 446 (2024), 109681. DOI: 10.1016/j.aim.2024.109681
On monic abelian cubics, Compositio Mathematica (3) 158 (2022), 550-567. DOI: 10.1112/S0010437X22007369
On the representation of k-free integers by binary forms, joint work with C. L. Stewart, Revista Matematica Iberoamericana (2) 37 (2021), 723-748. DOI: 10.4171/rmi/1213
The number of quartic D4-fields with monogenic cubic resolvent ordered by conductor, joint work with Cindy Tsang, Transactions of the American Mathematical Society (3) 374 (2021), 1987-2033. DOI: 10.1090/tran/8260
On prime values of binary quadratic forms with a thin variable, joint work with P. C. H. Lam and D. Schindler, Journal of the London Mathematical Society (2) 102 (2020), 749-772. DOI: 10.1112/jlms.12336
Zeroes of polynomials with prime inputs and Schmidt’s h-invariant, joint work with Shuntaro Yamagishi, Canadian Journal of Mathematics (3) 72 (2020), 805-833. DOI: 10.4153/S0008414X19000026
On binary quartic forms with bounded invariants and small Galois groups, joint work with Cindy Tsang, Pacific Journal of Mathematics (1) 302 (2019), 249-291. DOI: 10.2140/pjm.2019.302.249
On binary cubic and quartic forms, Journal de Th´eorie des Nombres de Bordeaux, (2) 31 (2019), 323-341. DOI: 10.5802/jtnb.1083
On the representation of integers by binary forms, with C. L. Stewart, Mathematische Annalen 375 (2019), 133-163. DOI: 10.1007/s00208-019-01855-y
Density of power-free values of polynomials, with Kostadinka Lapkova, Mathematika 65 (2019), 1038-1050. DOI: 10.1112/S0025579319000275
Square-free values of decomposable forms, Canadian Journal of Mathematics 70 (2018), 1390-1415. DOI: 10.4153/CJM-2017-060-4
Power-free values of binary forms and the global determinant method, International Mathematics Research Notices, 16 Volume 2017, 5078-5135. DOI: 10.1093/imrn/rnw165
Submitted papers (by date of submission):
Hilbert's tenth problem for systems of diagonal quadratic forms, and Büchi's problem https://arxiv.org/abs/2412.16740 (2025)
On the number of binary quadratic forms having discriminant 1−4p, p prime, with Alison Beth Miller, https://arxiv.org/abs/2011.06559 (2025)
Exponential sums over singular binary quartic forms and applications, with Yasuhiro Ishitsuka, Takashi Taniguchi, and Frank Thorne https://arxiv.org/abs/2404.00541 (2024)